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We present the Julia package HomotopyContinuation.jl, which provides an algorithmic framework for solving polynomial systems by numerical homotopy continuation. We introduce the basic capabilities of the package and demonstrate the software…

Mathematical Software · Computer Science 2018-05-31 Paul Breiding , Sascha Timme

Julia is a mature general-purpose programming language, with a large ecosystem of libraries and more than 12000 third-party packages, which specifically targets scientific computing. As a language, Julia is as dynamic, interactive, and…

In this paper we present GridapTopOpt, an extendable framework for level set-based topology optimisation that can be readily distributed across a personal computer or high-performance computing cluster. The package is written in Julia and…

Mathematical Software · Computer Science 2026-01-26 Zachary J. Wegert , Jordi Manyer , Connor Mallon , Santiago Badia , Vivien J. Challis

The increasing importance of Computational Science and Engineering has highlighted the need for high-quality scientific software. However, research software development is often hindered by limited funding, time, staffing, and technical…

Software Engineering · Computer Science 2025-03-10 Armin Ariamajd , Raquel López-Ríos de Castro , Andrea Volkamer

We present NEP-PACK a novel open-source library for the solution of nonlinear eigenvalue problems (NEPs). The package provides a framework to represent NEPs, as well as efficient implementations of many state-of-the-art algorithms. The…

Numerical Analysis · Mathematics 2018-11-26 Elias Jarlebring , Max Bennedich , Giampaolo Mele , Emil Ringh , Parikshit Upadhyaya

Robotics programming typically involves a trade-off between the ease of use offered by Python and the run-time performance of C++. While multi-language architectures address this trade-off by coupling Python's ergonomics with C++'s speed,…

Robotics · Computer Science 2024-06-07 Gustavo Nunes Goretkin , Joseph Carpinelli , Andy Park

The solutions of a system of polynomials in several variables are often needed, e.g.: in the design of mechanical systems, and in phase-space analyses of nonlinear biological dynamics. Reliable, accurate, and comprehensive numerical…

Mathematical Software · Computer Science 2019-07-02 Jasmine Otto , Angus Forbes , Jan Verschelde

GPUs are popular devices for accelerating scientific calculations. However, as GPU code is usually written in low-level languages, it breaks the abstractions of high-level languages popular with scientific programmers. To overcome this, we…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-04-13 Tim Besard , Pieter Verstraete , Bjorn De Sutter

Technical computing is a challenging application area for programming languages to address. This is evinced by the unusually large number of specialized languages in the area (e.g. MATLAB, R), and the complexity of common software stacks,…

Programming Languages · Computer Science 2018-08-13 Jeff Bezanson , Jake Bolewski , Jiahao Chen

PHCpack is a large software package for solving systems of polynomial equations. The executable phc is menu driven and file oriented. This paper describes the development of phcpy, a Python interface to PHCpack. Instead of navigating…

Mathematical Software · Computer Science 2014-04-30 Jan Verschelde

The Julia programming language has gained acceptance within the High-Performance Computing (HPC) community due to its ability to tackle two-language problem: Julia code feels as high-level as Python but allows developers to tune it to…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-04-17 Sergio Sanchez-Ramirez , Mosè Giordano

Computational methods are driving high impact microscopy techniques such as ptychography. However, the design and implementation of new algorithms is often a laborious process, as many parts of the code are written in close-to-the-hardware…

Computer Vision and Pattern Recognition · Computer Science 2022-07-27 Francesco Guzzi , George Kourousias , Fulvio Billè , Roberto Pugliese , Alessandra Gianoncelli , Sergio Carrato

Program synthesis -- the automatic generation of code given a specification -- is one of the most fundamental tasks in artificial intelligence (AI) and the dream of many programmers. Numerous synthesizers have been developed for program…

We present ForwardDiff, a Julia package for forward-mode automatic differentiation (AD) featuring performance competitive with low-level languages like C++. Unlike recently developed AD tools in other popular high-level languages such as…

Mathematical Software · Computer Science 2016-07-28 Jarrett Revels , Miles Lubin , Theodore Papamarkou

High-level scripting languages are in many ways polar opposites to GPUs. GPUs are highly parallel, subject to hardware subtleties, and designed for maximum throughput, and they offer a tremendous advance in the performance achievable for a…

Software Engineering · Computer Science 2013-04-23 Andreas Klöckner , Nicolas Pinto , Bryan Catanzaro , Yunsup Lee , Paul Ivanov , Ahmed Fasih

Geometric computing with chain complexes allows for the computation of the whole chain of linear spaces and (co)boundary operators generated by a space decomposition into a cell complex. The space decomposition is stored and handled with…

Computational Geometry · Computer Science 2017-11-07 Francesco Furiani , Giulio Martella , Alberto Paoluzzi

Development of scientific software involves tradeoffs between ease of use, generality, and performance. We describe the design of a general hyperbolic PDE solver that can be operated with the convenience of MATLAB yet achieves efficiency…

We present QuantumToolbox$.$jl, an open-source Julia package for simulating open quantum systems. Designed with a syntax familiar to users of QuTiP (Quantum Toolbox in Python), it harnesses Julia's high-performance ecosystem to deliver fast…

Quantum Physics · Physics 2025-10-06 Alberto Mercurio , Yi-Te Huang , Li-Xun Cai , Yueh-Nan Chen , Vincenzo Savona , Franco Nori

There is a need for open-source libraries in emission tomography that (i) use modern and popular backend code to encourage community contributions and (ii) offer support for the multitude of reconstruction techniques available in recent…

The library scikit-fda is a Python package for Functional Data Analysis (FDA). It provides a comprehensive set of tools for representation, preprocessing, and exploratory analysis of functional data. The library is built upon and integrated…

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